This paper presents a new coding scheme that considerably increases the efficiency of the channel in multicast setting. Specifically, we study the scenario where three terminals exchange their messages via a satellite gateway. The main difference between the proposed scheme and conventional three-way relay channel is the use of joint channel and network coding. This allows three terminals to transmit simultaneously, therefore, reducing the number of time slots. In our scheme, the relay may either amplify and forward or de-noise and forward, whereas in the conventional scheme the relay decodes and performs bit-wise exclusive OR on the packets or simply decodes the bit-wise XOR of the two messages and broadcasts it to all terminals. So while conventional schemes assume a binary channel on the downlink, we assume a ternary channel on the downlink. Furthermore, while in the conventional scheme each terminal removes its own message from the downlink signal in order to recover the other terminal's message, in our scheme after removing its own message, a terminal can decode a second terminal's encoded message treating the third terminal message as interference and finally recover the third terminal's message interference-free. We show that our scheme achieves a total rate of 2.
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